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TheCarg'eseSummerSchool"Sound-?owinteractions"washeldinthe-
stitutd'EtudesScienti?quesdeCarg'eseinCorsica,Francefrom19thJune
to1stJuly,2000.
Theunderstandingofsoundand?owinteractionshasmadesomerema-
ableprogresssincethepioneeringworksoftheRussianandBritishschools,
inthe1950s. Inaddition,thegrowingavailabilityduringthepast10years
ofsophisticatedcomputer/electronics/materialstechniquesallowsforthe-
velopmentofagrowingnumberofapplicationsaswellasthepossibilityof
addressingnewfundamentalproblems. Thecouplingbetweenacousticwaves
and?owmotionisbasicallynonlinear,sothatthesoundpropagationand
generationismodi?edbythe?owandthe?owcanalsobemodi?edbythe sound.
Asaresult,thisproblemisinvestigatedinmanydi?erentscienti?c
communities,suchasappliedmathematics,acousticsand?uidmechanics,
amongothers. Inouropinion,thetimehadcometotrytogatherthe-
searchersinthedi?erentcommunitiestogetherinatutorialenvironemnt.
So,
thisschoolbroughttogetherworldwidespecialistsinordertopresentvarious
aspectsofsound-?owinteractions,andshareexpertiseandmethodologiesso
astopromotecross-fertilisation.
ThebasicknowledgeintheareaisintroducedbyA. HirschbergandC. Schram.
Hepresentstheaeroacousticsofinternal?owinaverylivelyway
withalotofillustrationdevices. Heintroducesaeroacousticanalogiesand
applicationslikemusicalinstruments,theRijketube,speechproductionetc.
M. S. Howeintroducesthetheoryofvortexsoundinaverydidacticway. From
Lighthill'sacousticanalogy,heshowshowvorticityandentropy?uctuations
canbeseenassourcesofsound. Then,usingthecompactGreen'sfunctions,
heshowshowtocomputethevortexsound. Asanexampleofthemethod
presented,heappliesthistheorytopressuretransientsgeneratedbyhi-
speedtrains. F. Lundgivesthebasicequationsofsound-?owinteractions.
Thenheintroducesveryclearlythescatteringofsoundbecauseofvorticity
andgivesthemostrecentresultsonultrasoundpropagationthroughadis-
dered?ow. V. Ostashevpresentsgeometricalacousticsinmovingmediaand
theimportantpracticalproblemofsoundpropagationinturbulence(at-
sphere,ocean). A. Fabrikantexaminestheplasma-hydrodynamicsanalogies
includingtheresonantwave-?owinteractioninshear?ows,wavesofnegative
VI Preface energyandover-re?ectionandacousticoscillatorsin?uid?ows.
P. J. Mor-
sondescribesthedynamicsofthecontinuousspectrumwhichoccursinshear
?ow. Theresultsareinterpretedinthecontextofin?nitedimensionalHam-
toniansystemstheory. G. Chagelishvilipresentsnewlinearmechanismsof
acousticwavegenerationinsmoothshear?owsusinganon-modalstudy. N.
Peakepresents?uid-structureinteractionsinthepresenceofmean?ows,
includingtheproblemsofinstabilityandcausality. Finally,W.
Lauterborn
presentsnonlinearacousticswithapplicationstosonoluminescenceandto
acousticchaos.
InthisCarg'eseSummerSchool,54studentsfrom12nations,and11l-
turersfrom7nationsparticipated. Aknowledgements.
TheSummerSchoolandthispublicationwouldnot havebeenpossiblewithout:
*?nancialsupportfromtheEuropeanUnion,theCentreNationaldela
RechercheScienti?que,theMinist'eredesA?airesEtrang'eres,theM-
ist'eredel'EducationNationale,delaRechercheetdelaTechnologieand
theGroupementdeRecherche"Turbulence"; *the guidance of Elisabeth
Dubois-Violette, director of the Institut
d'EtudesScienti?quesdeCarg'ese;
*thehelpofChantalAriano,NathalieBedjai,BrigitteCassegrain,Pierre-
EricGrossiandthewholeteaminpreparingandhostingofthisschool.
Finally,wewishtothankthelecturersforgivingsomuchtimeinprep-
ingthelecturesandwritingthemup,aswellasmakingthemselvesavailable
fordiscussionsduringtheschool. 1 LeMans,Paris,Lyon YvesAur'egan , 2
September2001 Agn'esMaurel , 1 VincentPagneux , 3
Jean-Fran,coisPinton . 1
Laboratoired'Acoustiquedel'Universit'eduMaine,UMRCNRS6613, Av.
OMessiaen,72085LeMansCedex9,France 2
LaboratoireOndesetAcoustique,UMRCNRS7587,
ESPCI,10rueVauquelin,75005Paris,France 3
LaboratoiredePhysique,UMRCNRS1325,
EcoleNormaleSup'erieuredeLyon,46all'eed'Italie,69007Lyon,France
Preface VII
SomeofthelecturersoftheCarg'eseSchool,fromlefttoright:M. S. Howe,A.
Hirschberg,P. Morrison,W. Lauterborn,V. Ostashev,A. Fabrikant,N.
Peake, T. Colonius(PhotoC. Schram)
SomeoftheparticipantsoftheCarg'eseSchool(PhotoC. Schram)
TableofContents APrimitiveApproachtoAeroacoustics
AvrahamHirschberg,ChristopheSchram...1 1 Introduction ...1 2
FluidDynamics ...2 3 Lighthill'sAnalogy...4 4 JetNoise ...7 5
Thermo-Acoustics ...9 6 AcousticalEnergy ...10 7 Rijke-Tube...11 8
Vortex-SoundTheory ...14 9 ChoiceoftheGreen'sFunction...17 10
Howe'?owinteractions,andshareexpertiseandmethodologiesso
astopromotecross-fertilisation.
ThebasicknowledgeintheareaisintroducedbyA. HirschbergandC. Schram.
Hepresentstheaeroacousticsofinternal?owinaverylivelyway
withalotofillustrationdevices. Heintroducesaeroacousticanalogiesand
applicationslikemusicalinstruments,theRijketube,speechproductionetc.
M. S. Howeintroducesthetheoryofvortexsoundinaverydidacticway. From
Lighthill'sacousticanalogy,heshowshowvorticityandentropy?uctuations
canbeseenassourcesofsound. Then,usingthecompactGreen'sfunctions,
heshowshowtocomputethevortexsound. Asanexampleofthemethod
presented,heappliesthistheorytopressuretransientsgeneratedbyhi-
speedtrains. F. Lundgivesthebasicequationsofsound-?owinteractions.
Thenheintroducesveryclearlythescatteringofsoundbecauseofvorticity
andgivesthemostrecentresultsonultrasoundpropagationthroughadis-
dered?ow. V. Ostashevpresentsgeometricalacousticsinmovingmediaand
theimportantpracticalproblemofsoundpropagationinturbulence(at-
sphere,ocean). A. Fabrikantexaminestheplasma-hydrodynamicsanalogies
includingtheresonantwave-?owinteractioninshear?ows,wavesofnegative
VI Preface energyandover-re?ectionandacousticoscillatorsin?uid?ows.
P. J. Mor-
sondescribesthedynamicsofthecontinuousspectrumwhichoccursinshear
?ow. Theresultsareinterpretedinthecontextofin?nitedimensionalHam-
toniansystemstheory. G. Chagelishvilipresentsnewlinearmechanismsof
acousticwavegenerationinsmoothshear?owsusinganon-modalstudy. N.
Peakepresents?uid-structureinteractionsinthepresenceofmean?ows,
includingtheproblemsofinstabilityandcausality. Finally,W.
Lauterborn
presentsnonlinearacousticswithapplicationstosonoluminescenceandto
acousticchaos.
InthisCarg'eseSummerSchool,54studentsfrom12nations,and11l-
turersfrom7nationsparticipated. Aknowledgements.
TheSummerSchoolandthispublicationwouldnot havebeenpossiblewithout:
*?nancialsupportfromtheEuropeanUnion,theCentreNationaldela
RechercheScienti?que,theMinist'eredesA?airesEtrang'eres,theM-
ist'eredel'EducationNationale,delaRechercheetdelaTechnologieand
theGroupementdeRecherche"Turbulence"; *the guidance of Elisabeth
Dubois-Violette, director of the Institut
d'EtudesScienti?quesdeCarg'ese;
*thehelpofChantalAriano,NathalieBedjai,BrigitteCassegrain,Pierre-
EricGrossiandthewholeteaminpreparingandhostingofthisschool.
Finally,wewishtothankthelecturersforgivingsomuchtimeinprep-
ingthelecturesandwritingthemup,aswellasmakingthemselvesavailable
fordiscussionsduringtheschool. 1 LeMans,Paris,Lyon YvesAur'egan , 2
September2001 Agn'esMaurel , 1 VincentPagneux , 3
Jean-FranccoisPinton . 1
Laboratoired'Acoustiquedel'Universit'eduMaine,UMRCNRS6613, Av.
OMessiaen,72085LeMansCedex9,France 2
LaboratoireOndesetAcoustique,UMRCNRS7587,
ESPCI,10rueVauquelin,75005Paris,France 3
LaboratoiredePhysique,UMRCNRS1325,
EcoleNormaleSup'erieuredeLyon,46all'eed'Italie,69007Lyon,France
Preface VII
SomeofthelecturersoftheCarg'eseSchool,fromlefttoright:M. S. Howe,A.
Hirschberg,P. Morrison,W. Lauterborn,V. Ostashev,A. Fabrikant,N.
Peake, T. Colonius(PhotoC. Schram)
SomeoftheparticipantsoftheCarg'eseSchool(PhotoC. Schram)
TableofContents APrimitiveApproachtoAeroacoustics
AvrahamHirschberg,ChristopheSchram...1 1 Introduction ...1 2
FluidDynamics ...2 3 Lighthill'sAnalogy...4 4 JetNoise ...7 5
Thermo-Acoustics ...9 6 AcousticalEnergy ...10 7 Rijke-Tube...11 8
Vortex-SoundTheory ...14 9 ChoiceoftheGreen'sFunction...17 10
Howe'sEnergyCorollary ...20 11
TheOpenPipeTerminationofanUn?angedPipe ...21 12
Whistler-NozzleandHumanWhistling ...25 13 Conclusion...27
References...28 LecturesontheTheoryofVortex-Sound MichaelS.
Howe...31 1 AerodynamicSound...31 1. 1
Lighthill'sAcousticAnalogy(1952)...31 1. 2
AerodynamicSoundfromLow-Mach-NumberTurbulence
ofUniformMeanDensity...34 1. 3
AerodynamicSoundfromLow-Mach-NumberTurbulence
ofVariableMeanDensity...35 2 VorticityandEntropyFluctuations
asSourcesofSound...37 2. 1
TheRoleofVorticityinLighthill'sTheory...37 2. 2
AcousticAnalogyinTermsoftheTotalEnthalpy...39 2. 3
VorticityandEntropySources...40 3
FundamentalSolutionsoftheWaveEquation...43 3. 1
TheHelmholtzEquation...43 3. 2 TheWaveEquation...46 4
GeneralSolutionoftheInhomogeneousWaveEquation...47 4. 1
GeneralSolutionintheFrequency-Domain...47 X TableofContents 4. 2
GeneralSolutionintheTime-Domain...49 5 CompactGreen'sFunctions...
The coupling between acoustic waves and fluid flow motion is basically nonlinear, with the result that flow and sound modify themselves reciprocally with respect to generation and propagation properties. As a result this problem is investigated by many different communities, such as applied mathematics, acoustics and fluid mechanics. This book is the result of an international school which was held to discuss the foundation of sound--flow interactions, to share expertise and methodologies, and to promote cross-fertilization between the different disciplines involved. It consists essentially of a set of pedagogical lectures and is meant to serve not only as a compact source of reference for the experienced researcher but also as an advanced textbook for postgraduate students, and nonspecialists wishing to familiarize themselves in depth, at a research level, with this fascinating subject.
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